Convert 1 011 110 100 100 869 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 1 011 110 100 100 869(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
1 011 110 100 100 869 to a signed binary in one's (1's) complement representation?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 1 011 110 100 100 869 ÷ 2 = 505 555 050 050 434 + 1;
  • 505 555 050 050 434 ÷ 2 = 252 777 525 025 217 + 0;
  • 252 777 525 025 217 ÷ 2 = 126 388 762 512 608 + 1;
  • 126 388 762 512 608 ÷ 2 = 63 194 381 256 304 + 0;
  • 63 194 381 256 304 ÷ 2 = 31 597 190 628 152 + 0;
  • 31 597 190 628 152 ÷ 2 = 15 798 595 314 076 + 0;
  • 15 798 595 314 076 ÷ 2 = 7 899 297 657 038 + 0;
  • 7 899 297 657 038 ÷ 2 = 3 949 648 828 519 + 0;
  • 3 949 648 828 519 ÷ 2 = 1 974 824 414 259 + 1;
  • 1 974 824 414 259 ÷ 2 = 987 412 207 129 + 1;
  • 987 412 207 129 ÷ 2 = 493 706 103 564 + 1;
  • 493 706 103 564 ÷ 2 = 246 853 051 782 + 0;
  • 246 853 051 782 ÷ 2 = 123 426 525 891 + 0;
  • 123 426 525 891 ÷ 2 = 61 713 262 945 + 1;
  • 61 713 262 945 ÷ 2 = 30 856 631 472 + 1;
  • 30 856 631 472 ÷ 2 = 15 428 315 736 + 0;
  • 15 428 315 736 ÷ 2 = 7 714 157 868 + 0;
  • 7 714 157 868 ÷ 2 = 3 857 078 934 + 0;
  • 3 857 078 934 ÷ 2 = 1 928 539 467 + 0;
  • 1 928 539 467 ÷ 2 = 964 269 733 + 1;
  • 964 269 733 ÷ 2 = 482 134 866 + 1;
  • 482 134 866 ÷ 2 = 241 067 433 + 0;
  • 241 067 433 ÷ 2 = 120 533 716 + 1;
  • 120 533 716 ÷ 2 = 60 266 858 + 0;
  • 60 266 858 ÷ 2 = 30 133 429 + 0;
  • 30 133 429 ÷ 2 = 15 066 714 + 1;
  • 15 066 714 ÷ 2 = 7 533 357 + 0;
  • 7 533 357 ÷ 2 = 3 766 678 + 1;
  • 3 766 678 ÷ 2 = 1 883 339 + 0;
  • 1 883 339 ÷ 2 = 941 669 + 1;
  • 941 669 ÷ 2 = 470 834 + 1;
  • 470 834 ÷ 2 = 235 417 + 0;
  • 235 417 ÷ 2 = 117 708 + 1;
  • 117 708 ÷ 2 = 58 854 + 0;
  • 58 854 ÷ 2 = 29 427 + 0;
  • 29 427 ÷ 2 = 14 713 + 1;
  • 14 713 ÷ 2 = 7 356 + 1;
  • 7 356 ÷ 2 = 3 678 + 0;
  • 3 678 ÷ 2 = 1 839 + 0;
  • 1 839 ÷ 2 = 919 + 1;
  • 919 ÷ 2 = 459 + 1;
  • 459 ÷ 2 = 229 + 1;
  • 229 ÷ 2 = 114 + 1;
  • 114 ÷ 2 = 57 + 0;
  • 57 ÷ 2 = 28 + 1;
  • 28 ÷ 2 = 14 + 0;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

1 011 110 100 100 869(10) = 11 1001 0111 1001 1001 0110 1010 0101 1000 0110 0111 0000 0101(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 50.

  • A signed binary's bit length must be equal to a power of 2, as of:
  • 21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
  • The first bit (the leftmost) indicates the sign:
  • 0 = positive integer number, 1 = negative integer number

The least number that is:

1) a power of 2

2) and is larger than the actual length, 50,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


4. Get the positive binary computer representation on 64 bits (8 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64.


Decimal Number 1 011 110 100 100 869(10) converted to signed binary in one's complement representation:

1 011 110 100 100 869(10) = 0000 0000 0000 0011 1001 0111 1001 1001 0110 1010 0101 1000 0110 0111 0000 0101

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

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How to convert signed integers from the decimal system to signed binary in one's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in one's complement representation:

  • 1. If the number to be converted is negative, start with the positive version of the number.
  • 2. Divide repeatedly by 2 the positive representation of the integer number that is to be converted to binary, keeping track of each remainder, until we get a quotient that is equal to ZERO.
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above. Thus, the last remainder of the divisions becomes the first symbol (the leftmost) of the base two number, while the first remainder becomes the last symbol (the rightmost).
  • 4. Binary numbers represented in computer language must have 4, 8, 16, 32, 64, ... bit length (a power of 2) - if needed, fill in '0' bits in front (to the left) of the base 2 number calculated above, up to the right length; this way the first bit (leftmost) will always be '0', correctly representing a positive number.
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's.

Example: convert the negative number -49 from the decimal system (base ten) to signed binary one's complement:

  • 1. Start with the positive version of the number: |-49| = 49
  • 2. Divide repeatedly 49 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 49 ÷ 2 = 24 + 1
    • 24 ÷ 2 = 12 + 0
    • 12 ÷ 2 = 6 + 0
    • 6 ÷ 2 = 3 + 0
    • 3 ÷ 2 = 1 + 1
    • 1 ÷ 2 = 0 + 1
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:
    49(10) = 11 0001(2)
  • 4. The actual bit length of base 2 representation is 6, so the positive binary computer representation of a signed binary will take in this case 8 bits (the least power of 2 that is larger than 6) - add '0's in front of the base 2 number, up to the required length:
    49(10) = 0011 0001(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's:
    -49(10) = 1100 1110
  • Number -49(10), signed integer, converted from the decimal system (base 10) to signed binary in one's complement representation = 1100 1110